Existence of Solutions for <inline-formula> <graphic file="1029-242X-2010-968271-i1.gif"/></inline-formula>-Generalized Vector Variational-Like Inequalities

Abstract

We introduce and study a class of -generalized vector variational-like inequalities and a class of -generalized strong vector variational-like inequalities in the setting of Hausdorff topological vector spaces. An equivalence result concerned with two classes of -generalized vector variational-like inequalities is proved under suitable conditions. By using FKKM theorem, some new existence results of solutions for the -generalized vector variational-like inequalities and -generalized strong vector variational-like inequalities are obtained under some suitable conditions.